The latent heat of melting is the amount of energy needed to convert a solid substance at its melting temper-
ature to a liquid at the same temperature. For typical volcanic rocks, the latent heat of melting is around
5×105 J/kg, which means it takes 5×105 J to turn 1 kg of volcanic rock from solid at its melting temperature
to liquid at the same temperature. Assuming that providing the latent heat of melting is the only important
time-limiting step in turning Io’s rocks to liquid, how much time does it take to completely melt all of Io’s
crust? This is the resurfacing time for Io.
It seems to me that you need to know the thickness of the crust and how fast heat is added to it. This information is not provided.
To calculate the time it takes to completely melt Io's crust, we need to consider the following steps:
1. Determine the total mass of Io's crust: Let's assume the mass of Io's crust is M kg.
2. Calculate the total energy required to melt Io's crust: The latent heat of melting is given as 5×105 J/kg. Therefore, the total energy (E) required to melt Io's crust can be calculated as follows:
E = M × 5×105 J/kg
3. Determine the rate at which energy is being provided: Since providing the latent heat of melting is the only time-limiting step, we can assume that energy is being provided at a constant rate. Let's denote this rate as P J/s.
4. Calculate the time required to melt Io's crust: The time required to melt Io's crust (T) can be calculated using the formula:
T = E / P
Now, since the problem statement does not provide the value for Io's crust mass (M) or the rate at which the latent heat is being provided (P), we need these values to proceed with the calculation. Unfortunately, without this information, it is not possible to determine the specific time it takes to melt all of Io's crust.